Research Group of Prof. Dr. Frans R. Klinkhamer

Focus: fundamental aspects of elementary particle physics and structure of spacetime

Four main topics:

1. Baryon number violation through nonperturbative effects in the Electroweak Standard Model:

Sphalerons and spectral flow:

New results on spectral flow and sphalerons have been obtained in [Klinkhamer & Lee, 2001] and are under investigation.

Two reviews: [Klinkhamer, 2002; Klinkhamer & Rupp, 2003].

The sphaleron $\text{S}$ is related to the Adler-Bell-Bardeen anomaly. Over the years, it has become clear that there are more sphalerons. In fact, there also exists a sphaleron $\text{S}^{*}$ related to the $SU(2)$ Witten anomaly; see [Klinkhamer, 1993]. And, finally, there exists a sphaleron $\widehat{\text{S}}$ related to the $SU(3)$ Bardeen anomaly; see [Klinkhamer & Rupp, 2005; Klinkhamer & Nagel, 2017].

2. CPT anomaly:

Chiral gauge theories defined over a topologically nontrivial space manifold have an anomalous breaking of Lorentz and CPT invariance. An extensive review: [Klinkhamer, 2005].

3. Small-scale structure of spacetime:

The goal is to investigate a possible nontrivial structure of spacetime at very small length scales.


Two aspects have been considered in particular:

  1. The impact on the propagation of photons with wavelengths larger than the size of the "spacetime defects" (see, e.g., [Bernadotte & Klinkhamer, 2007; Klinkhamer & Schreck, 2008; Klinkhamer et al., 2017]).
  2. The detailed structure of one particular type of "spacetime defect" appearing as a soliton-type solution of the classical field equations (for a review, see [Klinkhamer, 2018]).

4. Vacuum energy and cosmology:

Since 1998, it has become clear that there is not one cosmological constant problem but that there are three:

  • Why is |ρvac| << (EPlanck)4 ?
  • Why is ρvac ≠ 0 ?
  • Why is now ρvac ∼ ρmatter ?

Taking Lorentz-invariance seriously (cf. recent UHECR bounds on Lorentz violation in the photon sector [Klinkhamer et al., 2017]), a new approach [Klinkhamer & Volovik, 2008] to this set of problems is based on the following assumption:

the perfect quantum vacuum can be considered to behave as a self-sustained Lorentz-invariant medium with a new type of conserved charge.

The argument is based solely on thermodynamics (cf. Einstein 1907) and has an analog in condensed-matter physics (Larkin-Pikin effect, 1969).

Recent results are reviewed in [Klinkhamer & Volovik, 2016; Klinkhamer & Volovik, 2019].

Some talks:
  1. Spacetime defects (Castiglioncello, September 2018)
  2. On an anomalous origin of Lorentz and CPT violation (Faro, 2017)
  3. A new approach to the cosmological constant problem (Seoul, October 2015; Update January 2019)
  4. Sphalerons and anomalies (an introduction) (Seoul, October 2015)
  5. Elementary particle physics and cosmology for engineers (and others) (Karlsruhe, February 2013)
  6. Superluminal neutrino: Theoretical considerations (Karlsruhe, December 2011)
  7. Towards a derivation of G (Bremen, July 2010)
  8. UHECR bounds on Lorentz violation in the photon sector (Penn State, August 2008)
  9. Lorentz noninvariance and neutrino oscillations (Belgium, February/March 2006)
  10. Electroweak baryon number violation: basic mechanism (Ann Arbor, June 2003)

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